We present MO:mb relations using mb(Pn) and mb(Lg) for earthquakes and explosions occurring in tectonic and stable areas. The observations for mb(Pn) range from about 3 to 6 show excellent separation between earthquakes and explosions on Mo:mb plots, independent of the magnitude. The scatter in Mo:mb observations for NTS explosions is small compared to the earthquake data. The MOmb(Lg) data for Soviet explosions overlay the observations for U.S. explosions. These results, and the small scatter for NTS explosions, suggest weak dependence of MO:mb relations on emplacement media. A simple theorical model is developed which matches all these observations. The model uses scaling similarity and conservation of energy to provide a physical link between seismic moment and a broadband seismic magnitude. Three factors, radiation pattern, material property, and apparent stress, contribute to the separation between earthquakes and explosions. This theoretical separation is independent of broadband magnitude. For U.S. explosions in different media, the material property and apparent stress contributions are shown to compensate for one another, supporting the observations that MO:mub is nearly independent of source geology. ¿American Geophysical Union 1993